Modeling an adiabatic quantum computer

Details Modeling an adiabatic quantum computer Modeling an adiabatic quantum computer

2007-01-22

arxiv.org/abs/quant-ph/0701161v1

Phys. Rev. Lett. 98, 120503 (2007)

Physics

Quantum Physics

8 pages 2 figures

Scientific paper

We map adiabatic quantum evolution on the classical Hamiltonian dynamics of a 1D gas (Pechukas gas) and simulate the latter numerically. This approach turns out to be both insightful and numerically efficient, as seen from our example of a CNOT gate simulation. For a general class of Hamiltonians we show that the escape probability from the initial state scales no faster than |\dot{\lambda}|^{\gamma}, where |\dot{\lambda}| is the adiabaticity parameter. The scaling exponent for the escape probability is \gamma = 1/2 for all levels, except the edge (bottom and top) ones, where \gamma <~1/3. In principle, our method can solve arbitrarily large adiabatic quantum Hamiltonians.

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